Given:
Molecular mass of compound before acylation = 180
Molecular mass of compound after acylation = 390
Number of amino groups in the compound before acylation = ?

Solution:
1. Find the molecular formula of the compound before acylation:
Let the molecular formula of the compound before acylation be CxHyNz.
The molecular mass of the compound can be written as:
molecular mass = (12x + 1y + 14z)

Substituting the given molecular mass of the compound before acylation:
180 = 12x + 1y + 14z
Equation 1: 12x + y + 14z = 180

2. Find the molecular formula of the compound after acylation:
Let the molecular formula of the compound after acylation be CxHyNzOa.
The molecular mass of the compound can be written as:
molecular mass = (12x + 1y + 14z + 16a + 12)

Substituting the given molecular mass of the compound after acylation:
390 = 12x + 1y + 14z + 16a + 12
Equation 2: 12x + y + 14z + 16a = 378

3. Find the difference between the two equations:
Subtracting equation 1 from equation 2, we get:
16a = 198
a = 12.375 (not a whole number, which means the compound does not have any oxygen atoms)

4. Find the value of z:
Substituting the value of a in equation 2, we get:
12x + y + 14z + 198 = 390
Equation 3: 12x + y + 14z = 192

Subtracting equation 1 from equation 3, we get:
3z = 12
z = 4

5. Find the value of x:
Substituting the values of y and z in equation 1, we get:
12x + 1y + 14z = 180
12x + 1y + 14(4) = 180
12x + y = 124

The compound must contain only whole number of atoms, so we need to find a combination of x and y that satisfy the above equation.
x = 10, y = 4 is one such combination.

6. Find the number of amino groups:
The molecular formula of the compound before acylation is C10H14N4.
The number of amino groups in the compound is equal to the number of nitrogen atoms, which is 4.

Therefore, the number of amino groups present per molecule of the former compound is 4.